Pattern-recognized structures in bounded turbulent shear flows

1977 ◽  
Vol 83 (4) ◽  
pp. 673-693 ◽  
Author(s):  
James M. Wallace ◽  
Robert S. Brodkey ◽  
Helmut Eckelmann
Keyword(s):  
Reynolds Stress ◽  
Coherent Structures ◽  
Shear Flows ◽  
Local Maximum ◽  
Total Sample ◽  
Turbulent Shear ◽  
Turbulence Structures ◽  
Signal Pattern ◽  
Turbulent Shear Flows ◽  
High Reynolds

It is now well established that coherent structures exist in turbulent shear flows. It should be possible to recognize these in the turbulence signals and to program a computer to extract and ensemble average the corresponding portions of the signals in order to obtain the characteristics of the structures. In this work only the u-signal patterns are recognized, using several simple criteria; simultaneously, however, the v or w signals as well as uv or uw are also processed. It is found that simple signal shapes describe the turbulence structures on the average. The u-signal pattern consists of a gradual deceleration from a local maximum followed by a strong acceleration. This pattern is found in over 65% of the total sample in the region of high Reynolds-stress production. The v signal is found to be approximately 180° out of phase with the u signal. These signal shapes can be easily associated with the coherent structures that have been observed visually. Their details have been enhanced by quadrant truncating. These results are compared with randomly generated signals processed by the same method.

Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures

2010 ◽  
Vol 661 ◽  
pp. 178-205 ◽  
Author(s):  
PHILIP HALL ◽  
SPENCER SHERWIN
Keyword(s):  
Coherent Structures ◽  
Shear Flows ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Streamwise Vortex ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Turbulent Shear Flows ◽  
External Flows

The relationship between asymptotic descriptions of vortex–wave interactions and more recent work on ‘exact coherent structures’ is investigated. In recent years immense interest has been focused on so-called self-sustained processes in turbulent shear flows where the importance of waves interacting with streamwise vortex flows has been elucidated in a number of papers. In this paper, it is shown that the so-called ‘lower branch’ state which has been shown to play a crucial role in these self-sustained processes is a finite Reynolds number analogue of a Rayleigh vortex–wave interaction with scales appropriately modified from those for external flows to Couette flow, the flow of interest here. Remarkable agreement between the asymptotic theory and numerical solutions of the Navier–Stokes equations is found even down to relatively small Reynolds numbers, thereby suggesting the possible importance of vortex–wave interaction theory in turbulent shear flows. The relevance of the work to more general shear flows is also discussed.

scholarly journals Frequency–wavenumber mapping in turbulent shear flows

2015 ◽  
Vol 783 ◽  
pp. 166-190 ◽  
Author(s):  
Roeland de Kat ◽  
Bharathram Ganapathisubramani
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Shear Flows ◽  
Spatial Scales ◽  
Turbulent Shear ◽  
Data Set ◽  
Frequency Spectra ◽  
Taylor’S Hypothesis ◽  
Turbulent Shear Flows ◽  
High Reynolds

Spatial turbulence spectra for high-Reynolds-number shear flows are usually obtained by mapping experimental frequency spectra into wavenumber space using Taylor’s hypothesis, but this is known to be less than ideal. In this paper, we propose a cross-spectral approach that allows us to determine the entire wavenumber–frequency spectrum using two-point measurements. The method uses cross-spectral phase differences between two points – equivalent to wave velocities – to reconstruct the wavenumber–frequency plane, which can then be integrated to obtain the spatial spectrum. We verify the technique on a particle image velocimetry (PIV) data set of a turbulent boundary layer. To show the potential influence of the different mappings, the transfer functions that we obtained from our PIV data are applied to hot-wire data at approximately the same Reynolds number. Comparison of the newly proposed technique with the classic approach based on Taylor’s hypothesis shows that – as expected – Taylor’s hypothesis holds for larger wavenumbers (small spatial scales), but there are significant differences for smaller wavenumbers (large spatial scales). In the range of Reynolds number examined in this study, double-peaked spectra in the outer region of a turbulent wall flow are thought to be the result of using Taylor’s hypothesis. This is consistent with previous studies that focused on examining the limitations of Taylor’s hypothesis (del Álamo & Jiménez, J. Fluid Mech., vol. 640, 2009, pp. 5–26). The newly proposed mapping method provides a data-driven approach to map frequency spectra into wavenumber spectra from two-point measurements and will allow the experimental exploration of spatial spectra in high-Reynolds-number turbulent shear flows.

Coherent Structures in Turbulent Shear Flows

1990 ◽  
Vol 43 (5S) ◽  
pp. S203-S209 ◽  
Author(s):  
J. M. Wallace ◽  
F. Hussain
Keyword(s):  
Coherent Structures ◽  
Shear Flows ◽  
Turbulent Shear ◽  
Turbulent Shear Flows ◽  
Kinematic Properties

What is firmly known about the kinematic properties and dynamic importance of coherent structures in bounded and unbounded turbulent shear flows is briefly summarized. The nature of instabilities giving rise to these structures is discussed. Unanswered questions requiring further research are posed.

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